A starting point strategy for nonlinear interior methods

A starting point strategy for nonlinear interior methods

This paper presents a strategy for choosing the initial point slacks and multipliers in interior methods for nonlinear programming It consists of rst computing a Newton like step to estimate the magnitude of these three variables and then shifting the slacks and multipliers so that they are su ciently positive The new strategy has the option of respecting the initial estimate of the solution gi...

Interior Point Methods for Nonlinear Optimization

Optimal Adjustment Algorithm for p Coordinates and the Starting Point in Interior Point Methods

Carla T. L. S. Ghidini, Aurelio R. L. Oliveira, Jair Silva Institute of Mathematics, Statistics and Scientific of Computation (IMECC), State University of Campinas (UNICAMP), São Paulo, Brazil Federal University of Mato Grosso do Sul (UFMS), Mato Grosso do Sul, Brazil E-mail: {carla, aurelio}@ime.unicamp.br, [email protected] Received September 15, 2011; revised October 16, 2011; accepted Octobe...

Interior-point methods for nonconvex nonlinear programming: cubic regularization

In this paper, we present a barrier method for solving nonlinear programming problems. It employs a Levenberg-Marquardt perturbation to the Karush-Kuhn-Tucker (KKT) matrix to handle indefinite Hessians and a line search to obtain sufficient descent at each iteration. We show that the Levenberg-Marquardt perturbation is equivalent to replacing the Newton step by a cubic regularization step with ...

Interior point methods for large-scale nonlinear programming

In the contribution, we describe an algorithm for solving nonlinear nonconvex programming problems, which is based on the interior point approach. The main theoretical results concern direction determination and step-length selection. We split inequality constraints into active and inactive parts to overcome problems with instability. Inactive constraints are eliminated directly, while active c...